1. Field of the Invention
This invention relates in general to the field of scanning interferometry and, in particular, to a new approach for measuring sample deformations occurring during interferometric measurements.
2. Description of the Prior Art
Recent developments in micro-optics and micro-electro-mechanical systems (MEMS) technology produced a variety of engineered micro-elements, ranging from gears and mirror arrays to membranes, resonators and accelerators. Inasmuch as these micro-elements (which vary in size from micrometers to millimeters) are susceptible to shape changes while in operation, a need has arisen for measuring not only their static shape but also their motion behavior (that is, the vertical displacement due to operational motion and shape changes due to vibration, deformation, and the like).
Traditional surface profilometry has dealt with the characterization of the surface profile of a static object. In scanning interferometric measurements, the surface of the object is scanned vertically (that is, the direction normal to the plane of the test surface) to produce interferograms that are acquired as the optical path difference between the object and a reference mirror is varied. In accordance with conventional terminology, the term “out-of-plane” is used in this disclosure to refer to the direction of scanning (regarding the sample object's surface displacement). The term “object motion” is used to refer to the cumulative out-of-plane displacement of the surface of the test object as a result of its operational motion and other external influences, such as vibration, deformation, etc. Object motion is not intended to include the motion resulting from scanning of the test object.
For the purposes of this disclosure, object motion is considered slow when it is negligible for shape-measurement detection, so that the object can be considered static (both conditions that are present in conventional profilometry). Such slow, quasi-static, motion can arise, for example, from thermal or pressure loading, or from creeping or shrinkage. The frequency of such slow motion is much lower than the sampling rate of the detecting system. Fast motion, on the other hand, is characterized by frequencies much higher than that of the sampling system and typically arises from a shock wave propagating through the object as a result of mechanical impact, or from the application of a high-frequency voltage pulse, as is the case in MEMS operation.
The range of motion (which may also be referred to as the dynamic range of motion or amplitude) is another relevant characteristic of object motion and it can be described, for example, in units of wavelength of light. The dynamic range of object motion depends on the object's mechanical and operational characteristics and may range, for instance, from fractions of a wavelength, for small vibrations and stress deformations that are essential for MEMS-membrane operation, to several tens of a wavelength or more for micro-mirror movements that find their use in tunable photonic devices.
Several techniques have been reported that can be used for limited measurements of different types of object motion, such as digital holography (applicable to reflecting and scattering surfaces), and digital speckle pattern interferometry (DSPI) and electro-optic holography (both used for scattering surfaces). These techniques are limited in their applicability by the relatively long data-transfer times associated with area detectors. Another technique is Doppler vibrometry (for example, see Albrecht et al., “Laser Doppler and Phase Doppler Measurement Techniques,” Springer-Verlag, 2002), which is based on heterodyne interferometry and utilizes fast detection of deformations at a single point (single-point detection). The limitation of this technique lies in the fact that the relative phase of vibrations at consecutive data points can be lost and therefore the recovery of object-motion information may be incorrect. All of these prior-art approaches can be used with continuous as well as stroboscopic illumination.
Other interferometric and fringe-projection techniques are described by Michael Pawlowski et al. in “Shape and motion measurement of time-varying three-dimensional objects based on spatiotemporal fringe-pattern analysis,” Opt. Eng. 41(2) 450-459 (2002), and Xavier Colonna de Lega et al. in “Deformation measurement with object-induced dynamic phase shifting,” Applied Optics, Vol. 35, No. 25, 5115-5121 (1996). These articles teach that fringes representing deformation can be analyzed when phase change is in an appropriate range.
The optical profilometric techniques traditionally used to determine object shape based on spatial or temporal analysis of fringe patterns are not always suitable for detecting object motion, as herein defined, because of phase-change constraints inherent with the algorithms associated with each technique. The discrepancy between the actual size of the measurement phase change introduced by object motion and the nominal size (the phase step) assumed and required by the algorithms used to perform interferometric analysis may prevent the use of the algorithms with any degree of reliability. For example, a conventional five-step phase algorithm (such as the Schwider/Hariharan algorithm) is based on a phase step of π/2±ε (typically about 5 degrees) between acquisition frames during the interferometric scan. If the object motion materially alters the actual phase change between the object and the reference surfaces, the algorithm will produce unreliable results. Thus, conventional profilometry is inadequate to measure motion when the object motion is characterized by a range of amplitudes or frequencies that are not suitable for the algorithms utilized in the system (and thus the information cannot be processed in converging fashion to describe the object motion).
Recent profilometric technique improvements, such as the use of a reference signal (described in U.S. Publication No. 2002-0196450, incorporated here by reference), addressed measurement precision but did not provide an avenue of compensation for object motion. Although the use of a reference signal makes it possible to correct scanner deviations from nominal performance, the computational constraints of the algorithms still prevent its general application in the measurement of object motion.
Conventional interferometric applications rely on precise measurements or knowledge of the changing optical path difference (OPD) between the test object and the reference surface as a result of scanning (or any equivalent method utilized to introduce a fringe shift, such as fringe projection techniques, wavelength shifting, polarization techniques, change of index of refraction in optical path, etc.). Specifically, the change in OPD (also commonly referred to in the art as “fringe shift”) between frames and the corresponding change in phase (normally referred to as the “phase step”) are used to calculate surface height. In the case of ideal scanning of a static object (i.e., scanning without motion errors of the scanner due to back-lashes, friction, etc.), the phase step will remain constant between sampling frames as determined by the scanner's design velocity profile (for example, 90 degrees at the mean wavelength used for illumination, including the effect of the angle of illumination). As such, the phase-versus-time plot is a straight line with a slope that corresponds to the constant design speed of the scanner, as illustrated in FIG. 1. As mentioned, the algorithms utilized for analysis allow deviations from ideal scanning behavior so long as the phase change remains within a predetermined “operational window,” which is illustrated in the figure for each scanner step by the area bound by the upper and lower limit traces (straight dashed lines) around the phase plot. For instance, for a 90-degree phase-step algorithm, such an operational window may correspond to a phase step of π/2±ε (the width of the operational window, typically about ±5 degrees, is illustrated disproportionately large for illustration).
If a sinusoidal object motion were present with an amplitude that caused the phase steps to remain within the operational window of the algorithm, as illustrated in FIG. 2 by the vertical phase-change window associated with each scanning step, it would still be possible to retrieve the object motion from conventional interferometric analysis because the algorithm would provide a measure of the phase change between acquisition frames, which in turn could be used in conventional manner to calculate the motion of the test surface in relation to the sample stage. On the other hand, if the object motion were more pronounced (such as, for example, characterized by a constant linear component and a harmonic component), the actual phase changes might not always be within the operational window of the algorithm, as illustrated in FIG. 3 (wherein the linear and sinusoidal components of the object motion are represented by straight dotted and sinusoidal continuous lines, respectively, and the phase change is shown outside the operational window for all steps except n+1). Accordingly, interferometric analysis would not allow accurate recovery of the object motion.
Therefore, to the extent that interferometric profilers are used for object characterization, conventional analysis approaches do not generally allow for proper monitoring of object motion on the basis of actual scanner position history. This invention provides a solution to this problem and achieves sub-wavelength accuracy in object motion measurements through the use of non-contact, optical methods.